The problem, is there a causal or non causal correlation between the smoke point and the viscosity temperature-dependence for the cooking and vegetable oils.

It is true only for high unsaturated oils because saturated oils (that usually used for frying) will not have significant changes in viscosity while the changes in smoke point might be substantial.

I agree these answers, and I add questions: Is it true that the smoke point is less than the boiling point of some oils ?

The smoke point of a vegetable oil is related to the presence of free fatty acids presence in the vegetable oil during frying. Higher the ffa, lower the smoke point and the oil before catching fire, generally starts smoking.  High viscous oils generally have high smoking and fire points which is influenced by its chemical composition such as ffa and gums. 

Viscosity is a function of temperature. At frying temperatures, usually the differences become less betweeen oils. Highly saturated fats have high smoke point and the converse, highly unsaturated oils will have lower smoke points. During our experiments, we generally found that unrefined vegetable oils have lower smoke points than their refined counterparts. This has been implicated for the presence of ffa and the gums by the refining industry and hence these are removed as soap and wet gum sludges.